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A speaker enclosure side is what engineers call a plate, as opposed to say a beam or a shell. The problem of deflection has been solved for a long time for various geometries, loadings and boundary conditions. The appropriate case for speaker enclosures is the rectangular plate with clamped or built in edges. The equations I will be discussing come from a text shown in one of the attachments. There is a stiffness parameter usually called D which applies to all plates. It is shown in an attachment. It is the product of the Modulus of Elasticity E, sometimes called Young's Modulus, the plate thickness cubed and divided by one minus Poisson's ratio squared. The main things to note about D are that Poisson's ratio is a small contributor and that E and thickness being cubed is more important. Table 35 lists the maximum deflection, at the center, for various ratios of short to long side in terms of a constant times the load times the short side to the fourth power divided by D. So, a thicker plate makes D larger and the deflection smaller. Inspection of the table shows that as the long side gets longer than the short side the constant asymptotes fairly quickly to the value for infinity and is approximately twice the deflection for the case when the sides are the same. If we take a case where an enclosure side is three times tall as it is wide and we put in two equally spaced so-called shelf braces, the side is split into three panels and the peak deflection of each is halved. If, on the other hand, a vertical brace parallel to the front and back were placed in the center of the side the constant would double, but the short side dimension would decrease by half which is a peak reduction by sixteen for a net peak deflection reduction of eight. Using two vertical braces the peak deflection reduction would be a factor of 81 for a net of about 40. All of this assumes the braces are not cut away so much as to lose their effectiveness. In terms of audibility its probably the average times the side area; but, without going through the calculations I expect the average to be of order one half. If you plan on doing your own calculations, note that the dimension a is a half dimension.
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A speaker enclosure side is what engineers call a plate, as opposed to say a beam or a shell. The problem of deflection has been solved for a long time for various geometries, loadings and boundary conditions. The appropriate case for speaker enclosures is the rectangular plate with clamped or built in edges. The equations I will be discussing come from a text shown in one of the attachments. There is a stiffness parameter usually called D which applies to all plates. It is shown in an attachment. It is the product of the Modulus of Elasticity E, sometimes called Young's Modulus, the plate thickness cubed and divided by one minus Poisson's ratio squared. The main things to note about D are that Poisson's ratio is a small contributor and that E and thickness being cubed is more important. Table 35 lists the maximum deflection, at the center, for various ratios of short to long side in terms of a constant times the load times the short side to the fourth power divided by D. So, a thicker plate makes D larger and the deflection smaller. Inspection of the table shows that as the long side gets longer than the short side the constant asymptotes fairly quickly to the value for infinity and is approximately twice the deflection for the case when the sides are the same. If we take a case where an enclosure side is three times tall as it is wide and we put in two equally spaced so-called shelf braces, the side is split into three panels and the peak deflection of each is halved. If, on the other hand, a vertical brace parallel to the front and back were placed in the center of the side the constant would double, but the short side dimension would decrease by half which is a peak reduction by sixteen for a net peak deflection reduction of eight. Using two vertical braces the peak deflection reduction would be a factor of 81 for a net of about 40. All of this assumes the braces are not cut away so much as to lose their effectiveness. In terms of audibility its probably the average times the side area; but, without going through the calculations I expect the average to be of order one half. If you plan on doing your own calculations, note that the dimension a is a half dimension. -
Barring catastrophe, or a very specific use-case, the audibility (panel resonance) is what matters -- not structural integrity. Increasing MoE is one way to achieve that, so I'll be curious how the common bracing techniques (e.g., shelf, window, other) affect audibility via that route. Fixity can also have a large impact on MoE, so butt joins vs. other methods (e.g., lock miter) might also be useful for you to examine -- both at the plate joins and at the bracing joins (e.g., does a dado make an audible difference or is it merely technique that aids assembly?).
Increasing the damping of the plate would be an alternate approach, but that is presumably outside of what you are trying to do here.Welcome to Rivendell, Mr. Anderson.
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